Erdős Problem 831

### What is the conjecture

https://www.erdosproblems.com/831

Let $h(n)$ be maximal such that in any $n$ points in $\mathbb{R}^2$ (with no three on a line and no four on a circle) there are at least $h(n)$ many circles of different radii passing through three points. Estimate $h(n)$.

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start with the conjecture linked at https://www.erdosproblems.com/831; the issue names no repository file, test, or entry point. Identify the project's established location and validation workflow for adding a formalized conjecture, and consider the work done when this conjecture is represented in Lean and the relevant checks pass.

Written by the indexing model from the issue text.